PSI - Issue 23

M.N. James et al. / Procedia Structural Integrity 23 (2019) 613–619 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

5

617

0.0018

CT1 (R=0.6) CT2 (R=0.1)

0.0016

da/dN = 0.2706 Δ CTOD p R² = 0.9836

0.0014

0.0012

0.0010

0.0006 da/dN (mm/cycle) 0.0008

0.0004

0.0002

0.0000

0

0.001 0.002 0.003 0.004 0.005 0.006 0.007

Δ CTOD p (mm)

Fig. 4. Plot of crack growth rate, da/dN, versus the plastic range of CTOD, ∆ CTODp, for tests on Grade 2 titanium at low (R = 0.1) and high (R = 0.6) stress ratio values. 4. Options to calculate the effective range of ∆ K CJP There are several possibilities to characterise the driving force for crack growth, or the effective range of stress intensity factor using the CJP model of crack tip stresses and the sensible way to decide which is the most appropriate is to compare their ability to characterise data from fatigue crack growth rate tests at several stress ratios using a statistical regression analysis. The equations proposed for the calculation of ∆ K CJP by, for example, Yang et al - equation 1 (Yang, Vasco-Olmo et al. 2018) and Nowell et al - equation 2 (Nowell, Dragnevski et al. 2018), as well as simply using the range of K F , if K R is deemed to be a secondary influence in alloys which do not exhibit substantial amounts of plasticity-induced shielding. ∆ = ( , − , ) − ( , − , ) (1) Equation 1 is based on the assumption that a positive value of K R acts to retard growth, based on the original assumption in its derivation that the positive direction for K R is opposite to that of crack growth. When K R is negative, it will therefore act to accelerate crack growth. = ( + ) (2) ∆ = , − , (3) The data in Fig. 5 show the crack growth rate data, obtained at two stress ratio values of 0.1 and 0.6 for Grade 2 titanium alloy, plotted as a function of the effective driving force obtained using equations 1, 2 and 3. It is immediately clear that Equation 2 leads to a discontinuous fitting, reflecting the much higher value of K F necessary to drive crack growth rates at the higher R value. Thus equation 2 does not provide the required single correlation line for crack growth rate at different stress ratio values. A regression analysis was then performed on the data obtained using equations 1 and 3. This analysis was performed in SigmaPlot software using a cubic order polynomial. The regression coefficient r obtained with equation 1 was 0.9950 with a standard error of estimate 4.74E-8, while for equation 3 the